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 | import trigo
import math
import numpy as np
class Plane(object):
    def __init__(self, a, b, c=None, d=None):
        if c !=None :
            if d != None :
                self._planeFromABCD(a,b,c,d)
            else :
                self._planeFrom3Points(a,b,c)
        else :
            self._planeFromVectorPoint(a, b)
 
    def _planeFromABCD(self, a, b,c,d):
        self._plane=[a, b, c, d]
 
    def _planeFrom3Points(self, a, b, c):
        u=[a[i]- b[i] for i in range(len(a))]
        v=[c[i]- b[i] for i in range(len(c))]
        w=trigo.vdot(u,v)
        return self.__planeFromVectorPoint(w, a)
 
 
    def _planeFromVectorPoint(self, v, p):
        self._plane=v+[-trigo.dot(v,p)]
 
    def __str__(self):
        plane=self._plane
        return "<{:8.3f},{:8.3f},{:8.3f},{:8.3f}>".format(
                plane[0], plane[1], plane[2], plane[3])
 
    def normalize(self):
        nn=self.norm()
        return [self._plane[i]/nn for i in range(4)]
 
    def norm(self):
        from math import sqrt
        return sqrt(sum([self._plane[i]*self._plane[i] for i in range(3)]))
 
    def perpendicular(self):
        return self._plane[:3]
 
    def distance(self, point):
        plane=self._plane
        return plane[0]*point[0]+plane[1]*point[1]+plane[2]*point[2]+plane[3]
 
    def check(self, points):
        print "check distance to plane"
        for v in points:
            dist=self.distance(v)
            print v, dist
 
if __name__ == "__main__":
    p1=Plane([1,0,0], [1,1,1])
    print "p1", p1
 
    p=Plane(1,2,0,2)
    print "p:", p
    print "norme de p:", p.norm()
    print "perpendiculaire a p:", p.perpendicular()
    print "p normalise",p.normalize() | 
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